Study On Vibration Control Of Flexible Beam Systems

The developing society is requiring high accuracy control performance.Owing to their good properties like lightweight and high efficiency,flexible structures have found important applications in intelligent manufacturing,transportation and aerospace fields.These structures could be considered as kinds of flexible beams due to their large lengthto-diameter ratio.As a result,it is worth researching control technology on flexible beam systems.However,the performance of the beam systems reduces severely due to their vibration.Therefore,vibration suppression becomes a significant problem in the application of flexible beam systems.Two flexible beams are studied in this thesis.One is a typical Euler-bernoulli beam.The other is a rotating length-varying flexible beam.In order to achieve more accurate dynamic responses,the flexible beam systems are modeled in infinite dimension and are described by hybrid partial differential equations and ordinate differential equations.Backstepping technique and iterative learning control are combined to put forward a backstepping-iterative learning control scheme for vibration suppression of the Eulerbernoulli beam.The author employs S-curve acceleration/deceleration scheme to regulate the extending speed of the rotating length-varying beam.Observer is developed to deal with the unknown disturbances.With the assistance of the observer,two control laws are designed to manage the vibration suppression and angular position tracking problems of the rotating length-varying beam system.The main contributions are presented as follows:1.In order to reach accurate dynamic responses and avoid the spillover effect,Hamilton's principle is employed for the flexible beam systems' mathematics description in infinite dimension.The flexible beams are modeled by hybrid partial differential equations and ordinate differential equations.2.Boundary control for the Euler-bernoulli beam system subjected to unknown disturbance is studied.Based on the infinite dimensional mathematic model and Lyapunov's synthesis method,a backstepping term and an iterative term are designed to reduce the vibration and attenuate the effect of the unknown disturbance.With the proposed control scheme,boundedness of closed-loop system states and convergence of the system output are proved via Lyapunov theory.Simulations are provided to demonstrate the effectiveness of the proposed scheme.3.Vibration suppression and angular position tracking problems of the flexible rotating length-varying beam system are studied.S-curve acceleration/deceleration scheme is employed for speed regulation of the length-varying beam.Novel observer is developed to estimate two unknown disturbances.With assistance of observer,two boundary control laws are put forward to manage vibration suppression and angular position tracking of the proposed beam system.Through Lyapunov's theory,the closed-loop system is proved to be bounded.Numerical simulations have displayed the effectiveness of the observers and boundary control laws.